पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/२९५

97 by means of one, to which the interest thereon for the (given) time is added, (happens to be the required) capital; and the interest required is the combined sum minus this capital. CHAPTER VI-MIXED PROBLEMS. An example in illustration thereof. 22. If one lends out money at the rate of 5 per cent (per month), the combined sum of interest and capital becomes 48 in 12 months. What are the capital and the interest therein ? Again another rule for the separation of the capital and the interest from their combined sum :- 23. The product of the given time and the rate-interest, divided by the rate-time and the rate-capital and then combined with one, is the divisor of the combined sum of the capital and interest; the resulting quotient has to be understood as the (required) capital. An example in illustration thereof. 24. Having given out on interest some money at the rate of 2 per cent (per mensem), one obtams 33 in 4 months as the combined sum (of the capital and the interest). What may be the capital (therein) ? The rule for the separation of the time and the interest from their combined sum :- 25. Take the rate-capital multiplied by the rate-time and divided by the rate-interest and by the given capital, and then combine this (resulting quantity) with one; then the quotient obtained by dividing the combined sum (of the time and interest) hy this (resulting sum) indeed becomes the (required) interest. Examples in illustration thereof. 26. Money amounting to 60 exactly was lent out at the rate of 5 per cent (per month) by one desirous of obtaining interest. [txI 23. Synbolically c= m +[x+1}. It is evident that this is very much the same as the formula given under 21. Cx2 25 Symbolically += m = - {²x7 +¹] = +1 = 2, where mit. 13